Digital Signal Processing Reference
In-Depth Information
N
N
r
ij
2
,
J
MU-FPC
(
w
k
(
n
))
=
J
FPC
(
w
k
(
n
))
+
γ
(5.111)
i
=
1
j
=
1
j
=
i
where
γ is the decorrelation factor
r
ij
=
E
y
i
(
is the cross-correlation between the
i
th and
j
th outputs
y
j
(
n
)
n
)
Furthermore, we can adapt the decorrelation weight γ, as discussed in
the Section 5.4.1.2, in order to increase the convergence rate and decrease
steady-state error. The adaptation procedure of the algorithm for the
k
th user
becomes
J
FPC
w
k
(
N
w
k
(
n
+
1
)
=
w
k
(
n
)
−
μ
∇
n
)
−
γ
(
n
)
r
ik
(
n
)
p
i
(
n
)
,
(5.112)
i
=
1
i
=
k
where
r
ik
(
n
)
is the
(
i
,
k
)
element of matrix
R
yy
(
n
)
p
i
(
n
)
is the
i
th column of matrix
P
(
n
)
Such matrices may be computed as
y
H
R
yy
(
n
+
1
)
=
ς
R
yy
(
n
)
+
(
1
−
ς
)
y
(
n
)
(
n
)
(5.113)
y
H
P
(
n
+
1
)
=
ς
P
(
n
)
+
(
1
−
ς
)
x
(
n
)
(
n
)
,
where
y
)
=
y
1
(
)
T
is the output vector
(
n
n
)
···
y
N
(
n
is a forgetting factor
ς
The decorrelation weight is updated by [65]
N
1
2
r
k
(
n
)
=
|
r
ik
|
N
−
1
i
=
1
(5.114)
i
=
k
γ
(
n
)
=
tanh [
r
k
(
n
)
]
For space-time multiuser processing, it is also necessary to guarantee
decorrelation of the signals in a time interval in order to remove the ISI. With
that in mind, the criterion becomes [63]
